1980 450SEL W116

I am having an issue with restarting my car immediately warm/hot to about 5 minutes after shutting it down. The car starts great cold. If I drive to the gas station or if I shut it down warm or hot and immediately try to restart it, it won't fire up and I've noticed that I do NOT hear the fuel pump hum like I do when I start it up cold. I no longer try to start it now warm/hot until I've sat for over 5 minutes and when I toggle the key I hear the fuel pump hum (if I don't hear it hum, I turn the key off because I know it won't start), and at that point it fires right up.

*Should I always hear the fuel pump hum briefly before a start?

*Does this sound like a fuel pump relay going bad?

*Does this sound like a fuel pump going bad?

*Is there a temp sensor that prevents the fuel pump from running?

*Could this be a problem with the safety switch air flow sensor plate?

*Could a bad OVP relay be the problem?

*Could a bad O2 sensor be the problem?

*Could the warm up compensator (WUC) be the problem?

*Could the RPM sensor be the problem?

*Also, where is the fuse for the Fuel Pump Relay? Is it number 4? I can't find any reference to its location nor my particular problem.

Heading out to start testing. Thanks for any and all replies!